Keeping in mind that I am studying to become a physicist, but not specifically a cosmologist (though I have had some graduate course-level work on the subject), I can only tell you with certainty that there is no real controversy over the issue that the speed of light has been very close to constant over most of the age of the universe, but at the instant of the Big Bang (i.e. the inflationary epoch) it may have been (or may not have been) quite different. There is little controversy over whether or not the Big Bang actually happened; as we literally see the "afterglow" (i.e. cosmic background radiation); we see the kinetic expansion (i.e. cosmic expansion/galactic redshift); and the nuclear synthesis models of the Big Bang give the correct ratio of hydrogen<->helium observed in the universe; no other model explains these things correctly. As you point out, the model is not perfect; the debates are fierce as to what occurred during the opening moments of the Big Bang, and perhaps the further-reaching consequences of General Relativity (i.e. the dark energy problem you pointed out earlier).
As far as the total age of the universe goes, you point out, basically, that we can't know because we haven't been around long enough to know. I won't try to argue with that (you really can't!) However, what we do see is a universe with the appearance of great age; for the speed of light to have varied by "orders of magnitude", a lot of observations would have to have "conspired" to produce the difference. Could one produce a model that could explain a young universe? It may be possible, but such a model would be enormously more complicated than the one we work with. In science, the simplest model prevails, even though the "simplest" model may still be complex indeed.
What did God really do to make the universe? I don't know. No one really does. All we mere humans can do is create models to explain natural cause and effect - that is what science is all about. "Belief" in a scientific model is inconsequential, IMHO; it just has to work to empirically explain observations. If people could realize this, I think much of the debate between science and religion could be peacefully resolved.
Thank you for your thoughtful post. Since I have run out of time on this round of freeping, it appears that the 4th graders' soccer strategy worked. Bummer.
I would like to encourage you in the same manner that I encouraged another Physics student about 10 years ago. He was looking for an area to explore in Physics to do his PhD and I suggested that the speed of light showed signs of not being a constant. If he had pursued my suggestion, he'd be at the top of his game right now. So here is my similar suggestion to you: Don't take for granted those points at the far end of the graph. If they all "conspire", it could mean that they are all dependent upon some variable that we have not yet discovered. One of the greatest physicists in our generation, Richard Feynman, won the Nobel prize following this line of attack. I'll reprint some of his story here, which I found also posted online at
http://www.zag.si/~jank/public/misc/joking_feynman.txt
The 7 Percent Solution
The problem was to find the right laws of beta decay. There appeared to be two particles, which were called a tau and a theta. They seemed to have almost exactly the same mass, but one disintegrated into two pions, and the other into three pions. Not only did they seem to have the same mass, but they also had the same lifetime, which is a funny coincidence. So everybody was concerned about this.
....
At that particular time I was not really quite up to things: I was always a little behind. Everybody seemed to be smart, and I didn't feel I was keeping up. Anyway, I was sharing a room with a guy named Martin Block, an experimenter. And one evening he said to me, "Why are you guys so insistent on this parity rule? Maybe the tau and theta are the same particle. What would be the consequences if the parity rule were wrong?"
....
So I got up and said, "I'm asking this question for Martin Block: What would be the consequences if the parity rule was wrong?"
Murray Gell-Mann often teased me about this, saying I didn't have the nerve to ask the question for myself. But that's not the reason. I thought it might very well be an important idea.
....
Finally they get all this stuff into me, and they say, "The situation is so mixed up that even some of the things they've established for years are being questioned -- such as the beta decay of the neutron is S and T. It's so messed up. Murray says it might even be V and A."
I jump up from the stool and say, "Then I understand EVVVVVERYTHING!"
They thought I was joking. But the thing that I had trouble with at the Rochester meeting -- the neutron and proton disintegration: everything fit but that, and if it was V and A instead of S and T, that would fit too. Therefore I had the whole theory!
That night I calculated all kinds of things with this theory. The first thing I calculated was the rate of disintegration of the muon and the neutron. They should be connected together, if this theory was right, by a certain relationship, and it was right to 9 percent. That's pretty close, 9 percent. It should have been more perfect than that, but it was close enough.
....
I was very excited, and kept on calculating, and things that fit kept on tumbling out: they fit automatically, without a strain. I had begun to forget about the 9 percent by now, because everything else was coming out right.
....
The next morning when I got to work I went to Wapstra, Boehm, and Jensen, and told them, "I've got it all worked out. Everything fits."
Christy, who was there, too, said, "What beta-decay constant did you use?"
"The one from So-and-So's book."
"But that's been found out to be wrong. Recent measurements have shown it's off by 7 percent."
Then I remember the 9 percent. ....
I went out and found the original article on the experiment that said the neutron-proton coupling is T, and I was shocked by something. I remembered reading that article once before (back in the days when I read every article in the Physical Review -- it was small enough). And I remembered, when I saw this article again, looking at that curve and thinking, "That doesn't prove anything!"
You see, it depended on one or two points at the very edge of the range of the data, and there's a principle that a point on the edge of the range of the data -- the last point -- isn't very good, because if it was, they'd have another point further along. And I had realized that the whole idea that neutron-proton coupling is T was based on the last point, which wasn't very good, and therefore it's not proved. I remember noticing that!
And when I became interested in beta decay, directly, I read all these reports by the "beta-decay experts," which said it's T. I never looked at the original data; I only read those reports, like a dope. Had I been a good physicist, when I thought of the original idea back at the Rochester Conference I would have immediately looked up "how strong do we know it's T?" -- that would have been the sensible thing to do. I would have recognized right away that I had already noticed it wasn't satisfactorily proved.
Since then I never pay any attention to anything by "experts." I calculate everything myself. When people said the quark theory was pretty good, I got two Ph.D.s, Finn Ravndal and Mark Kislinger, to go through the whole works with me, just so I could check that the thing was really giving results that fit fairly well, and that it was a significantly good theory. I'll never make that mistake again, reading the experts' opinions. Of course, you only live one life, and you make all your mistakes, and learn what not to do, and that's the end of you.